M\'ethode des orbites et formules du caract\`ere pour les repr\'esentations temp\'er\'ees d'un groupe alg\'ebrique r\'eel r\'eductif non connexe

TL;DR

This paper parametrizes irreducible tempered characters of non-connected reductive real Lie groups using Kirillov's formulas and descent methods, extending known results to non-connected cases.

Contribution

It provides a new parametrization of tempered characters for non-connected reductive real Lie groups, generalizing previous work on connected groups.

Findings

Parametrization of irreducible tempered characters for non-connected groups

Use of Kirillov's formulas and descent methods near elliptic elements

Extension of known results from connected to non-connected groups

Abstract

Let G be a non-connected reductive real Lie group. In this paper, I parametrize the set of irreductible tempered characters of G. Afterwards, I describe these characters by means of some ``Kirillov's formulas'', using the descent method near each elliptic element in G. If G is linear and connected, the parameters that I use are ``final basic'' parameters in the sense of Knapp and Zuckerman.